Sure, let's determine the mean, median, and mode of the given ages.
### Mean
The mean is calculated by adding all the ages together and then dividing by the number of ages.
To find the mean:
1. Sum all the ages: [tex]\(21 + 41 + 20 + 23 + 24 + 33 + 37 + 42 + 23 + 29 = 293\)[/tex]
2. Divide by the number of ages (10): [tex]\(293 / 10 = 29.3\)[/tex]
So, the mean age is [tex]\(29.3\)[/tex].
### Median
The median is the middle value of the ages when they are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.
To find the median:
1. Arrange the ages in ascending order:
[tex]\[
20, 21, 23, 23, 24, 29, 33, 37, 41, 42
\][/tex]
2. As there are 10 ages (even number), the median will be the average of the 5th and 6th numbers.
3. The 5th and 6th numbers are 24 and 29.
So, the median age is [tex]\((24 + 29)/2 = 26.5\)[/tex].
### Mode
The mode is the age that appears most frequently.
To find the mode:
1. Identify the age that appears most frequently from:
[tex]\[
20, 21, 23, 23, 24, 29, 33, 37, 41, 42
\][/tex]
The mode is [tex]\(23\)[/tex] since it appears twice, more frequently than any other ages.
### Summary
[tex]\[
\begin{tabular}{|l|l|}
\hline Mean & 29.3 \\
\hline Median & 26.5 \\
\hline Mode & 23 \\
\hline
\end{tabular}
\][/tex]
